Search results for "Normal Distribution"
showing 10 items of 135 documents
Parametric and nonparametric methods to generate time-varying surrogate data.
2009
We present both nonparametric and parametric approaches to generating time-varying surrogate data. Nonparametric and parametric approaches are based on the use of the short-time Fourier transform and a time-varying autoregressive model, respectively. Time-varying surrogate data (TVSD) can be used to determine the statistical significance of the linear and nonlinear coherence function estimates. Two advantages of the TVSD are that it keeps one from having to make an arbitrary decision about the significance of the coherence value, and it properly takes into account statistical significance levels, which may change with time. Our simulation examples and experimental results on blood pressure …
A Highly Flexible Trajectory Model Based on the Primitives of Brownian Fields—Part II: Analysis of the Statistical Properties
2016
In the first part of our paper, we have proposed a highly flexible trajectory model based on the primitives of Brownian fields (BFs). In this second part, we study the statistical properties of that trajectory model in depth. These properties include the autocorrelation function (ACF), mean, and the variance of the path along each axis. We also derive the distribution of the angle-of-motion (AOM) process, the incremental traveling length process, and the overall traveling length. It is shown that the path process is in general non-stationary. We show that the AOM and the incremental traveling length processes can be modeled by the phase and the envelope of a complex Gaussian process with no…
Parameter optimization for amplify-and-forward relaying with imperfect channel estimation
2009
Cooperative diversity is a promising technology for future wireless networks. In this paper, we consider a cooperative communication system operating in an amplify-and-forward (AF) mode with an imperfectly-known relay fading channel. It is assumed that a pilot symbol assisted modulation (PSAM) scheme with linear minimum mean square estimator (LMMSE) is used for the channel estimation. A simple and easy-to-evaluate asymptotical upper bound (AUB) of the symbol-error-rate (SER) is derived for uncoded AF cooperative systems with quadrature amplitude modulation (QAM) constellations. Based on the AUB, we propose a criterion for the choice of parameters in the PSAM scheme, i.e., the pilot spacing …
Comparing Correlation Matrix Estimators Via Kullback-Leibler Divergence
2011
We use a self-averaging measure called Kullback-Leibler divergence to evaluate the performance of four different correlation estimators: Fourier, Pearson, Maximum Likelihood and Hayashi-Yoshida estimator. The study uses simulated transaction prices for a large number of stocks and different data generating mechanisms, including synchronous and non-synchronous transactions, homogeneous and heterogeneous inter-transaction time. Different distributions of stock returns, i.e. multivariate Normal and multivariate Student's t-distribution, are also considered. We show that Fourier and Pearson estimators are equivalent proxies of the `true' correlation matrix within all the settings under analysis…
Influence of Whole-Body Dynamics on 15N PISEMA NMR Spectra of Membrane Proteins: A Theoretical Analysis
2009
AbstractMembrane proteins and peptides exhibit a preferred orientation in the lipid bilayer while fluctuating in an anisotropic manner. Both the orientation and the dynamics have direct functional implications, but motions are usually not accessible, and structural descriptions are generally static. Using simulated data, we analyze systematically the impact of whole-body motions on the peptide orientations calculated from two-dimensional polarization inversion spin exchange at the magic angle (PISEMA) NMR. Fluctuations are found to have a significant effect on the observed spectra. Nevertheless, wheel-like patterns are still preserved, and it is possible to determine the average peptide til…
Unveiling the Lewis Acid Catalyzed Diels–Alder Reactions Through the Molecular Electron Density Theory
2020
The effects of metal-based Lewis acid (LA) catalysts on the reaction rate and regioselectivity in polar Diels&ndash
COMPARATIVE ASSESSMENT OF SEVERAL MULTI-CRITERIA DECISION ANALYSIS TOOLS FOR MANAGEMENT OF CONTAMINATED SEDIMENTS
2007
Over the past several decades, environmental decision-making strategies have evolved into increasingly more sophisticated, information-intensive, and complexapproaches including expert judgment, cost-benefit analysis, toxicological risk assessment, comparative risk assessment, and a number of methods forincorporating public and stakeholder values. This evolution has led to an improved array of decision-making aids, including the development of Multi-CriteriaDecision Analysis (MCDA) tools that offer a scientifically sound decision analytical framework. The existence of different MCDA methods and the availability of corresponding software contribute to the possibility of practical implementat…
Multivariate nonparametric tests in a randomized complete block design
2003
AbstractIn this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and estimates are analogous to the traditional univariate methods. In test constructions, the univariate ranks are replaced by multivariate spatial ranks (J. Nonparam. Statist. 5 (1995) 201). Asymptotic theory is developed to provide approximations for the limiting distributions of the test statistics and estimates. Limiting efficiencies of the tests and treatment effect estimates are found in the…
Information Dynamics Analysis: A new approach based on Sparse Identification of Linear Parametric Models*
2020
The framework of information dynamics allows to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of a complex network. The information transfer from one process to another can be quantified through Transfer Entropy, and under the assumption of joint Gaussian variables it is strictly related to the concept of Granger Causality (GC). According to the most recent developments in the field, the computation of GC entails representing the processes through a Vector Autoregressive (VAR) model and a state space (SS) model typically identified by means of the Ordinary Least Squares (OLS). In this work, we propose a new identification …
Second-order interaction in a Trivariate Generalized Gamma Distribution
2004
The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).